Loop Group Decompositions in Almost Split Real Forms and Applications to Soliton Theory and Geometry
| dc.creator | Brander, David | |
| dc.date | 2008-05-14 | |
| dc.date.accessioned | 2026-07-07T12:23:33Z | |
| dc.date.available | 2026-07-07T12:23:33Z | |
| dc.description | We prove a global Birkhoff decomposition for almost split real forms of loop groups, when an underlying finite dimensional Lie group is compact. Among applications, this shows that the dressing action - by the whole subgroup of loops which extend holomorphically to the exterior disc - on the $U$-hierarchy of the ZS-AKNS systems, on curved flats and on various other integrable systems, is global for compact cases. It also implies a global infinite dimensional Weierstrass-type representation for Lorentzian harmonic maps (1+1 wave maps) from surfaces into compact symmetric spaces. An "Iwasawa-type" decomposition of the same type of real form, with respect to a fixed point subgroup of an involution of the second kind, is also proved, and an application given. | |
| dc.description | 12 Pages | |
| dc.identifier | https://arxiv.org/abs/0805.1979 | |
| dc.identifier | http://arxiv.org/abs/0805.1979 | |
| dc.identifier | J. Geom. Phys. 58 (2008) 1792-1800 | |
| dc.identifier | doi:10.1016/j.geomphys.2008.09.003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214028 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | 22E67, 37K10, 37K25 (Primary) 53C40 (Secondary) | |
| dc.title | Loop Group Decompositions in Almost Split Real Forms and Applications to Soliton Theory and Geometry | |
| dc.type | text |